Question: Which of the following numbers is a factor of 105? ${2,4,7,8,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $105$ by each of our answer choices. $105 \div 2 = 52\text{ R }1$ $105 \div 4 = 26\text{ R }1$ $105 \div 7 = 15$ $105 \div 8 = 13\text{ R }1$ $105 \div 14 = 7\text{ R }7$ The only answer choice that divides into $105$ with no remainder is $7$ $ 15$ $7$ $105$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $105$ $105 = 3\times5\times7 7 = 7$ Therefore the only factor of $105$ out of our choices is $7$. We can say that $105$ is divisible by $7$.